Dielectric metamaterials have shown potential for use in a broad range of applications in ultra-thin optical components including flat lenses, wave plates, polarizers, and nonlinear optical frequency converters. However, the realization of dielectric metamaterial resonators at visible and near infrared frequencies has heretofore been mostly limited to implementations in silicon, which emits light inefficiently because it is an indirect bandgap material. There remains a need to implement dielectric metamaterials in direct bandgap semiconductors so that the new functionalities and improved levels of performance offered by dielectric materials can be realized in active resonant optical devices such as LEDs, lasers, detectors, and modulators.